The paper is devoted to the development of a numerical algorithm for solving nonlinear integro-differential equations based on the use of quadrature formulas. The Koltunov-Rzhanitsyn kernel with weakly singular features of the Abel type is used as a kernel. To conduct a computational experiment, a computer program was developed; the results obtained by this program are reflected in the form of tables and graphs. A test example was solved, and the obtained approximate numerical results were compared with exact solutions. The influence of nonlinearity and integral parts on the nature of oscillatory process of a viscoelastic body was investigated.

Intensive garden yields and soil fertility are increased by giving liquid organic and mineral fertilizer locally to the soil. Each tree root system in the row is carried out on the basis of technical hydrodynamic legislation of the liquid pouring liquid organic fertilizer in the specified amount by opening the furrow next to it. Based on the results of the presented calculation, each tree is provided 10÷11L of liquid organic fertilizer to the root system in accordance with the aggregate movement speed, maintaining this mode was based on the dimensions of the working part and the capacity in it. Also it is presented the graphs of changes in the duration of pouring liquid organic fertilizer depending on the surface of the cracks, the rate of leakage and the rate of aggregation. Also, as a result of fertilization directly to the root of the tree, NDVI (Normalized Difference Vegetation Index) analysis was carried out through remote sensing techniques for monitoring development of surface fertilization and root system fertilization gardens, and the results revealed with a compartable NDVI map. According to NDVI analysis, fertilizing roots with liquid organic and minerals, development of intensive gardens had significantly positive with 7 percent comparing to other.

Vertical oscillations of three loads of different masses connected by nonlinear viscoelastic springs (suspensions) are considered in the paper. An account for rheological properties of the suspension, an integral model with the Koltunov-Rzhanitsyn relaxation kernel is used. Effective computational algorithms have been developed for solving problems based on the use of quadrature formulas. The effect of rheological properties of suspension on the mass displacement from the position of static equilibrium is investigated as well as the influence of nonlinear properties of the suspension on the mode of vibration and frequency.

No abstract

As an object of research, the technological process of cutting the roots of the stalks of the pine tree with the soil and placing them on the side together with the spherical disk in the combined aggregate implementation was accepted. In our republic's cotton cultivation field, the world's latest innovations, including minimal, resource-saving, Strip-till, No-till technologies of soil cultivation and drip irrigation methods, are gradually being introduced. Combined aggregates produced abroad and in our country, designed to perform several technological processes at once, are being supported and introduced by cotton growing clusters. We found it necessary to bring a combined aggregate that prepares new sedges and sedges in the fields with sedges. During the movement of the aggregate in the sedge field, the sedges of the sedge are first tilted to the side of the sedge, and the roots are trimmed with soil and placed at the bottom of the sedge. Then, the lower layer of the bush is divided into two parts, it is turned over the stalks laid on the sides, and new bushes are formed in that place. And in the place of existing puss, new furrows are formed. The research was carried out using methods and tools for measuring angles and distances and optimizing parameters using the mathematical planning method of multifactorial experiments. The study's results determined that the diameter of the spherical disk is 510 mm, the radius of curvature is 540 mm, and the installation angles relative to the direction of movement and the vertical should be 30-32° and 20°, respectively. The research results showed that it is possible to perform the technological processes of cutting the layer of the pistachio root with spherical disks and throwing it to the middle of the side.